Purchase this Material for $10

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
50 Videos

Determine whether each relation is a function, and state its domain and range.

Buy to View

Q1a

Determine whether each relation is a function, and state its domain and range.

```
\displaystyle
3x^2 + 2y =6
```

Buy to View

Q1b

Determine whether each relation is a function, and state its domain and range.

Buy to View

Q1c

Determine whether each relation is a function, and state its domain and range.

```
\displaystyle
x = 2^y
```

Buy to View

Q1d

A cell phone company charges a monthly fee of $30, plus $0.02 per minute of call time.

a) Write the monthly cost function, `C(t)`

, where t is the amount of time in minutes of call time during a month.

b) Find the domain and range of `C`

.

Buy to View

Q2

Graph `f(x) = 2|x + 3| -1`

, and state the domain and range.

Buy to View

Q3

Describe this interval using absolute value notation.

Buy to View

Q4

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

```
\displaystyle
f(x) =x^2
```

and ```
\displaystyle
g(x) = \sin x
```

Buy to View

Q5a

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

```
\displaystyle
f(x) =\frac{1}{x}
```

and ```
\displaystyle
g(x) = x
```

Buy to View

Q5b

For the pair of functions, give a characteristic that the two functions have in common and a characteristic that distinguishes them.

```
\displaystyle
f(x) =x^2
```

and ```
\displaystyle
g(x) = \sin x
```

Buy to View

Q5c

```
\displaystyle
f(x) =2^x
```

and ```
\displaystyle
g(x) = x
```

Buy to View

Q5d

Identify the intervals of increase/decrease, the symmetry, and the domain and rage of each function.

```
\displaystyle
f(x) = 3x
```

Buy to View

Q6a

Identify the intervals of increase/decrease, the symmetry, and the domain and range of each function.

```
\displaystyle
f(x) = x^2+ 2
```

Buy to View

Q6b

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

```
\displaystyle
f(x) =|x + 1|
```

Buy to View

Q7a

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

```
\displaystyle
f(x) = -0.25\sqrt{3(x+ 7)}
```

Buy to View

Q7b

For each of the following equations, state the parent function and the transformations that were applied. Graph the transformed function.

```
\displaystyle
f(x) = -2\sin(3x) + 1, 0 \leq x \leq 360^o
```

Buy to View

Q7c

```
\displaystyle
f(x) = 2^{-2x} -3
```

Buy to View

Q7d

The graph of `y = x^2`

is horizontally stretched by a factor of 2, reflected in the x—axis, and shifted 3 units down. Find the equation that results from the transformation, and graph it.

Buy to View

Q8

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = -f(-x)+2
```

Buy to View

Q9a

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y =f(-2(x+ 9)) - 7
```

Buy to View

Q9b

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y =f(x -2) + 2
```

Buy to View

Q9c

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = 0.3f(5(x-3))
```

Buy to View

Q9d

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = 1 -f(1-x)
```

Buy to View

Q9e

`(2, 1)`

is a point on the graph of `y =f(x)`

. Find the corresponding point on the graph of each of the following functions.

```
\displaystyle
y = -f(2(x - 8))
```

Buy to View

Q9f

For the point on a function, state the corresponding point on the inverse relation.

(1, 2)

Buy to View

Q10a

For the point on a function, state the corresponding point on the inverse relation.

(-1, -9)

Buy to View

Q10b

For the point on a function, state the corresponding point on the inverse relation.

(0, 7)

Buy to View

Q10c

For the point on a function, state the corresponding point on the inverse relation.

f(5) = 7

Buy to View

Q10d

For the point on a function, state the corresponding point on the inverse relation.

g(0) = -3

Buy to View

Q10e

For the point on a function, state the corresponding point on the inverse relation.

`h(1) = 10`

Buy to View

Q10f

Given the domain and range of a function, state the domain and range of the inverse relation.

`D = \{x\in \mathbb{R}\}`

, ```
\displaystyle
R = \{y \in \mathbb{R}, -2 < y < 2\}
```

Buy to View

Q11a

Given the domain and range of a function, state the domain and range of the inverse relation.

`D = \{x\in \mathbb{R}, x \geq 7\}`

, ```
\displaystyle
R = \{y \in \mathbb{R}, y < 12\}
```

Buy to View

Q11b

Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.

`f(x) = x^2 -4`

Buy to View

Q12a

Graph the function and its inverse relation on the same set of axes. Determine whether the inverse relation is a function.

`f(x) = 2^x`

Buy to View

Q12b

Find the inverse of each function.

`f(x) = 2x + 1`

Buy to View

Q13a

Find the inverse of each function.

`f(x) = x^3`

Buy to View

Q13b

Graph the following function. Determine whether it is discontinuous and, if so, where. State the domain and the range of the function.

```
\displaystyle
f(x) =
\begin{cases}
&2x, &\text{when } x < 1 \\
&x +1, &\text{when } x \geq 1
\end{cases}
```

Buy to View

Q14

Write the algebraic representation for the following piecewise function, using function notation.

Buy to View

Q15

If

```
\displaystyle
f(x) =
\begin{cases}
&x^2 +1, &\text{when } x < 1 \\
&3x, &\text{when } x \geq 1
\end{cases}
```

is `f(x)`

continuous at `x =1`

? Explain.

Buy to View

Q16

A telephone company charges $30 a month and gives the customer 200 free call minutes. After the 200 min, the company charges $0.03 a minute.

a) Write the function using function notation.

b) Find the cost for talking 350 min in a month.

c) Find the cost for talking 180 min in a month.

Buy to View

Q17

Given `f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}`

and `g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}`

, determine

`f(x) + g(x)`

Buy to View

Q18a

Given `f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}`

and `g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}`

, determine

`f(x)- g(x)`

Buy to View

Q18b

Given `f = \{(0, 6), (1, 3), (4, 7), (5, 8)\}`

and `g= \{(-1, 2), (1, 5), (2, 3) ,(4, 8), (8, 9)\}`

, determine

`f(x)\cdot g(x)`

Buy to View

Q18c

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`f`

Buy to View

Q19a

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`g`

Buy to View

Q19b

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`f +g`

Buy to View

Q19c

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`f -g`

Buy to View

Q19d

Given `f(x) = 2x^2 -2x, -2 \leq x \leq 3`

and `g(x) = -4x, -3 \leq x \leq 5`

, graph the following.

`fg`

Buy to View

Q19e

`f(x) = x^2 +2x`

and `g(x) = x + 1`

. Match the answer with the operation.

```
\displaystyle
\begin{array}{llllllll}
&(a) \phantom{.} x^3 + 3x^2 + 2x
&A \phantom{.} f(x) + g(x) \\
&(b) \phantom{.} -x^2 -x + 1
&B \phantom{.} f(x) - g(x) \\
&(c) \phantom{.} x^2 +3x + 1
&C \phantom{.} g(x) - f(x) \\
&(d) \phantom{.} x^2 +x - 1
&D \phantom{.} g(x) \times f(x)
\end{array}
```

Buy to View

Q20

`f(x) = x^3 +2x^2`

and `g(x) = -x + 6`

.

a) Complete the table.

b) Use the table to graph `f(x)`

and `g(x)`

on the same axes.

c) Graph (f 1 g)(x) on the same axes as part b).

d) State the equation of `(f + g)(x)`

.

e) Verify the equation of `(f + g)(x)`

using two of the ordered pairs in the table.

Buy to View

Q21